Proof of Modulational Instability of Stokes Waves in Deep Water

DOI10.1002/cpa.22073zbMath1526.76011arXiv2007.05018OpenAlexW3040744078WikidataQ113926663 ScholiaQ113926663MaRDI QIDQ6077896

Huy Quang Nguyen, Walter A. Strauss

Publication date: 18 October 2023

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.05018

zbMATH Keywords

linearizationHamiltonianconformal mappingthird-order asymptotic expansionnonlocal Dirichlet-Neumann operatorwater wave comprehensionZakharov-Craig-Sulem equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Hydrodynamic stability (76E99)

Related Items (8)

Quasiperiodic perturbations of Stokes waves: secondary bifurcations and stability ⋮ Benjamin-Feir instability of Stokes waves in finite depth ⋮ Transverse dynamics of two-dimensional traveling periodic gravity-capillary water waves ⋮ Nonlinear modulational instabililty of the Stokes waves in 2D full water waves ⋮ Modulational Instability of Classical Water Waves ⋮ On the analyticity of the Dirichlet-Neumann operator and Stokes waves ⋮ Benjamin-Feir instability of Stokes waves ⋮ Full description of Benjamin-Feir instability of Stokes waves in deep water

Cites Work

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• Asymptotic linear stability of solitary water waves
• On the Cauchy problem for gravity water waves
• Transverse instability of the line solitary water-waves
• On the water-wave equations with surface tension
• Numerical simulation of gravity waves
• Stability of small periodic waves for the nonlinear Schrödinger equation
• On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
• The modulational instability for a generalized Korteweg-de Vries equation
• Modulation instability: The beginning
• Nonlinear modulational instability of dispersive PDE models
• A proof of the Benjamin-Feir instability
• Modulational instability in nonlinear nonlocal equations of regularized long wave type
• Stability of Small Periodic Waves in Fractional KdV-Type Equations
• The instability of periodic surface gravity waves
• Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels
• Paralinearization of the Dirichlet to Neumann Operator, and Regularity of Three-Dimensional Water Waves
• Well-posedness of the water-waves equations
• Modulational Instability in the Whitham Equation for Water Waves
• The disintegration of wave trains on deep water Part 1. Theory
• Non-linear dispersion of water waves
• Stabilizing the Benjamin–Feir instability

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